Extended precision accumulator

CROSS-REFERENCE TO RELATED APPLICATIONS

0001This application is a divisional of U.S. application Ser. No. 09/788,685, titled “Extended Prevision Accumulator Operation”, filed Feb. 21, 2001; which is related to the following co-pending applications, each of which were also filed on Feb. 21, 2001: (1) U.S. application Ser. No. 09/788,683, titled “Partial Bitwise Permutations”; (2) U.S. application Ser. No. 09/788,670, titled “Binary Polynomial Multiplier”; (3) U.S. application Ser. No. 09/788,684, titled “Polynomial Arithmetic Operations”; and (4) U.S. application Ser. No. 09/788,682, titled “Configurable Instruction Sequence Generation”.

TECHNICAL FIELD

0002This invention relates to a microprocessor multiplier, and more particularly to a microcomputer multiplier with an extended precision accumulator.

BACKGROUND

0003Reduced instruction set computer (RISC) architectures were developed as industry trends tended towards larger, more complex instruction sets. By simplifying instruction set designs, RISC architectures make it easier to use techniques such as pipelining and caching, thus increasing system performance.

0004RISC architectures usually have fixed-length instructions (e.g., 16-bit, 32-bit, or 64-bit), with few variations in instruction format. Each instruction in an instruction set architecture (ISA) may have the source registers always in the same location. For example, a 32-bit ISA may always have source registers specified by bits 16–20 and 21–25. This allows the specified registers to be fetched for every instruction without requiring any complex instruction decoding.

SUMMARY

0005Cryptographic systems (“cryptosystems”) are increasingly used to secure transactions, to encrypt communications, to authenticate users, and to protect information. Many private-key cryptosystems, such as the Digital Encryption Standard (DES), are relatively simple computationally and frequently reducible to hardware solutions performing sequences of XORs, rotations, and permutations on blocks of data. Public-key cryptosystems, on the other hand, may be mathematically more subtle and computationally more difficult than private-key systems.

0006While different public-key cryptography schemes have different bases in mathematics, they tend to have a common need for integer computation across very large ranges of values, on the order of 1024 bits. This extended precision arithmetic is often modular (i.e., operations are performed modulo a value range), and in some cases polynomial instead of twos-complement. For example, RSA public-key cryptosystems use extended-precision modular exponentiation to encrypt and decrypt information and elliptic curve cryptosystems use extended-precision modular polynomial multiplication.

0007Public-key cryptosystems have been used extensively for user authentication and secure key exchange, while private-key cryptography has been used extensively to encrypt communication channels. As the use of public-key cryptosystems increases, it becomes desirable to increase the performance of extended-precision modular arithmetic calculations.

0008In one general aspect, a multiply unit is provided for use in a microprocessor having at least one general-purpose register for storing a predetermined number of bits. The multiply unit includes a multiplier and an extended-precision accumulator including more bits than each of the general-purpose registers.

0009Implementations include using the multiplier to provide a multiply-add operation whereby operands to the multiply unit are multiplied and added to the contents of the extended-precision accumulator. The multiplier may include an arithmetic multiplier and a polynomial multiplier.

0010In a polynomial multiplier implementation, a multiply-add operation multiplies two operands and adds the result to the contents of the extended-precision accumulator using an exclusive-or operation. In some implementations, the multiplier includes result logic for selecting which values to load into the extended-precision accumulator. For example, the result logic may be implemented as a multiplexer.

0011In some implementations, the extended-precision accumulator includes an extended register, a high-order register, and a low-order register. For example, the extended register may store 8-bit values and the other two registers may store 32-bit values. Instructions are provided for manipulating the contents of the extended-precision accumulator. One instruction moves a value from the extended-precision accumulator into a general-purpose register and an inverse instruction moves a value from a general-purpose register into the extended-precision accumulator. The instructions additionally may shift the contents of the extended-precision register.

0012The details of one or more implementations are set forth in the accompanying drawings and the description below. Other features and advantages will be apparent from the description and drawings, and from the claims.

DESCRIPTION OF DRAWINGS

0013<figref idref="DRAWINGS">FIG. 1</figref> is a block diagram of an exemplary five-stage pipeline that may be used in a RISC architecture.

0014<figref idref="DRAWINGS">FIG. 2</figref> is a block diagram of a processor core including an execution unit and a multiply unit.

0015<figref idref="DRAWINGS">FIG. 3</figref> is a diagram of data paths in an implementation of a multiply unit supporting binary polynomial arithmetic.

0016<figref idref="DRAWINGS">FIG. 4</figref> is a block diagram of multiplier arrays supporting arithmetic and binary polynomial multiplication in one implementation.

0017<figref idref="DRAWINGS">FIG. 5</figref> is a block diagram of an arithmetic multiplier array that may be used in the implementation shown in <figref idref="DRAWINGS">FIG. 4</figref>.

0018<figref idref="DRAWINGS">FIG. 6</figref> is a block diagram of a binary polynomial multiplier array that may be used in the implementation shown in <figref idref="DRAWINGS">FIG. 4</figref>.

0019<figref idref="DRAWINGS">FIG. 7A</figref> is a timing diagram showing the operation of 32-bit by 16-bit multiplies in one implementation.

0020<figref idref="DRAWINGS">FIG. 7B</figref> is a timing diagram showing the operation of 32-bit by 32-bit multiplies in one implementation.

0021<figref idref="DRAWINGS">FIG. 7C</figref> is a timing diagram showing the operation of divisions in one implementation.

0022<figref idref="DRAWINGS">FIG. 8</figref> is finite state machine implementing steps for performing multiply instructions.

0023<figref idref="DRAWINGS">FIG. 9</figref> is a finite state machine implementing steps for performing division instructions.

0024<figref idref="DRAWINGS">FIGS. 10A and 10B</figref> are instruction encodings for exemplary instructions manipulating an extended-precision multiplier.

DETAILED DESCRIPTION

0025Many public-key cryptosystems use extended-precision modular arithmetic to encrypt and decrypt data. For example, many elliptic curve (EC) cryptosystems extensively use polynomial multiplication and addition to encrypt and decrypt data. Performance of elliptic curve cryptosystems may be enhanced by modifying a programmable CPU multiplier to be responsive to newly defined instructions dedicated to polynomial operations.

0026When using elliptic curves defined over GF(2¹⁶³) (as recommended by the IEEE 1363-2000 standard), the main operation needed is multiplication over the field GF(2¹⁶³). Each of the 2¹⁶³elements can be represented as a polynomial of degree at most 163 with coefficients equal to 0 or 1. In this representation, two elements may be added using a simple bitwise XOR and two polynomials, a(X) and b(X), may be multiplied by computing a(X)b(X) mod P(X), where the product a(X)b(X) is a 326-degree polynomial, and P(X) is an irreducible polynomial as specified by the IEEE 1363-2000 standard.

0027Polynomial multiplication has the same form as modular multiplication, ab mod p, over the integers, except that: (1) regular addition is replaced by an XOR; and (2) regular 32-bit multiplication is replaced by a 32-bit carry-free multiplication. Therefore, polynomial modular multiplication may be performed using shifts and XORs instead of shifts and adds.

0028It is desirable to provide a multiply unit that supports fast polynomial multiplication and various other operations to increase the performance of cryptographic and other systems.

0029Providing support for extended precision modular arithmetic and polynomial operations can increase the performance of cryptosystems. Some cryptographic systems, such as those performing RSA cryptographic signature authentication, perform successive extended precision modular multiplications, accumulating the sum of the results. The performance of these systems may be increased by providing support in a multiply unit for an instruction to multiply two operands and add the result to an accumulator. When successive multiply/adds are performed, the accumulator may overflow. It is desirable to provide an extended precision accumulator to provide increased performance in cryptosystems and other systems.

0030Referring to <figref idref="DRAWINGS">FIG. 1</figref>, an exemplary microprocessor architecture that may be used to implement polynomial multiplication includes a five-stage pipeline in which an instruction may be issued each clock cycle and executed in a fixed amount of time, such as, for example, four clock cycles. The execution of each instruction is divided into five stages: instruction fetch (IF) stage <b>1001</b>, register read (RD) stage <b>1002</b>, arithmetic/logic unit (ALU) stage <b>1003</b>, memory (MEM) stage <b>1004</b>, and write back (WB) stage <b>1005</b>. In the IF stage <b>1001</b>, a specified instruction is fetched from an instruction cache. A portion of the fetched instruction is used to specify source registers that may be used in executing the instruction. In the read registers (RD) stage <b>1002</b>, the system fetches the contents of the specified source registers. These fetched values may be used to perform arithmetic or logical operations in the ALU stage <b>1003</b>. In the MEM stage <b>1004</b>, an executing instruction may read/write memory in a data cache. Finally, in the WB stage <b>1005</b>, values obtained by the execution of the instruction may be written back to a register.

0031Because some operations such as floating point calculations and integer multiply/divide, cannot always be performed in a single clock cycle, some instructions merely begin execution of an instruction. After sufficient clock cycles have passed, another instruction may be used to retrieve a result. For example, when an integer multiply instruction takes five clock cycles, one instruction may initiate the multiplication calculation, and another instruction may load the results of the multiplication into a register after the multiplication has completed. If a multiplication has not completed by the time a result is requested, the pipeline may stall until the result is available.

0032Referring to <figref idref="DRAWINGS">FIG. 2</figref>, an exemplary RISC architecture is provided by way of example. The processor core <b>2000</b> (also referred to as a “microprocessor core”) includes the following: an execution unit <b>2010</b>, a multiply/divide unit (MDU) <b>2020</b>, a system control coprocessor (CP<b>0</b>) <b>2030</b>, a memory management unit <b>2040</b>, a cache controller <b>2050</b>, and a bus interface unit (BIU) <b>2060</b>.

0033Execution unit <b>2010</b> is the primary mechanism for executing instructions within processor core <b>2000</b>. Execution unit <b>2010</b> includes a register file <b>2011</b> and an arithmetic logic unit (ALU) <b>2012</b>. In one implementation, the register file <b>2011</b> includes 32 32-bit general-purpose registers that may be used, for example, in scalar integer operations and address calculations. The register file <b>2011</b>, which includes two read ports and one write port, may be fully bypassed to minimize operation latency in the pipeline. ALU <b>2012</b> supports both logical and arithmetic operations, such as addition, subtraction, and shifting.

0034The MDU <b>2020</b> may be used to perform various operations including some or all of the following instructions described below: DIV, DIVU, MADD, MADDU, MFHI, MFLO, MSUB, MSUBU, MTHI, MTLO, MUL, MULT, MULTU, MFLHXU, MTLHX, MADDP, MULTP, and PPERM.

0035In one implementation, LO register <b>2023</b> and HI register <b>2022</b> are each 32 bits wide and function as dedicated output registers of MDU <b>2020</b>. In one implementation, ACX register <b>2021</b> provides 8 bits of additional integer precision beyond those provided by the HI/LO register pair. The precise number of bits is implementation dependent, with the preferred minimum size being 8 bits. For processors with 32-bit data paths, the preferred maximum size of the ACX register is 32 bits. In contrast, for processors with 64-bit data paths, the preferred maximum size of the ACX register is 64 bits. Hence, in a processor with 32-bit wide HI and LO registers, the combination of registers ACX/HI/LO can hold a concatenated value having more than 64 bits.

0036In the implementation described in <figref idref="DRAWINGS">FIGS. 2 and 3</figref>, the MDU <b>2020</b> includes a divide unit. However, other implementations provide a separate multiply and divide units implementing an extended accumulator in either the multiply unit, the divide unit, or in both the multiply and divide units.

0037The instructions MUL, MULT, and MULTU may be used to multiply two 32-bit numbers together. The result is stored in a specified register for MUL, and in the HI/LO registers for MULT and MULTU. For example, “MUL $7, $6, $5” multiplies the contents of registers $6 and $5 together and stores the result in register $7. The instruction “MULT $6, $5” multiplies the contents of registers $6 and $5 together and stores the result in the HI/LO registers. The MULTU instruction performs the same operation as MULT with MULTU applying to unsigned operands and MULT applying to signed operands. Additionally, the MULTU instruction clears the ACX register to all zeros.

0038The instructions DIV and DIVU perform division operations and store the results in the ACX/HI/LO registers. For example, “DIV $6, $5” divides the contents of register $6 by the contents of register $5 and stores the result in the ACX/HI/LO registers. The DIVU instruction performs the same operation on unsigned operands.

0039The instructions MSUB, MSUBU, MADD, and MADDU may be used to multiply the contents of two registers and then add or subtract the contents of the ACX/HI/LO registers. For example, “MSUB $6, $5” multiplies the contents of registers $6 and $5 together, subtracts the contents of the ACX/HI/LO registers from the result, and then stores the value in the ACX/HI/LO registers. The MADD instruction similarly multiplies the contents of two registers, adds the result to the ACX/HI/LO registers, and stores the result in the ACX/HI/LO registers. The MSUBU and MADDU perform the same operations on unsigned operands. In some implementations, the ACX register is not used in some operations and the contents of the ACX register following such operations may be undefined.

0040The MFHI, MFLO, MTHI, MTLO, MFLHXU, and MTLHX instructions are used to move data between the ACX/HI/LO registers and general-purpose registers. The first instruction, MFHI, loads the contents of the HI register into a general-purpose register. For example, “MFHI $5” loads the contents of the HI register into register $5. Similarly, MFLO loads the contents of the LO register into a general-purpose register. Conversely, the instructions MTHI and MTLO are used to load the contents of a general-purpose register into the HI or LO registers. For example, “MTHI $5” loads the contents of register $5 into the HI register.

0041More generally, an instruction format for MFLHXU (“Move From Extended Carry, Hi and Lo (Unsigned)”) is shown in <figref idref="DRAWINGS">FIG. 10A</figref>. When executed, the value in LO register <b>2023</b> is written into the general-purpose register “rd” specified by the instruction, as shown in <figref idref="DRAWINGS">FIG. 10A</figref>. The value in HI register <b>2022</b> is then written to LO register <b>2023</b>, the bits in ACX register <b>2021</b> are zero-extended and copied to HI register <b>2022</b>, and the ACX register bits are cleared. The number of ACX register bits is implementation dependent, and may range, for example, from 0 to 64 bits. If no ACX register bits are implemented in a particular implementation, the value of the ACX register will be taken to be zero.

0042Similarly, the instruction format for MTLHX (“Move to Lo, Hi and Extended Carry”) is shown in <figref idref="DRAWINGS">FIG. 10B</figref>. When executed, an appropriate number of bits (e.g., eight) of the value in HI register <b>2022</b> are written into the ACX register <b>2021</b>. The value in LO register <b>2023</b> is then written to the HI register, and the value in general-purpose register “rs” (specified by the instruction, as shown in <figref idref="DRAWINGS">FIG. 10B</figref>) is written to the LO register. This is the reverse of the operation of the MFLHXU instruction. Again, the number of ACX register bits is implementation dependent, and may range, for example, from 0 to 64 bits. If HI register <b>2022</b> contains more significant bits than the number implemented in ACX register <b>2021</b>, that information is discarded without raising an exception. If no ACX register bits are implemented, the move from the HI register to ACX register is taken as a “no-op”.

0043In one implementation, the content of the ACX register is not directly accessible. For purposes of discussion, in this implementation the ACX register is 8 bits wide, and the HI and LO registers are each 32 bits wide. To indirectly access the ACX register, the values stored in the ACX/HI/LO registers may be shifted to the left or right. For example, “MFLHXU $5” shifts contents of the ACX, HI, and LO registers to the right by one register position, loading the contents of the LO register into register $5. Thus, after performing the operation, the ACX register is zero, the HI register contains the previous contents of the ACX register, the LO register contains the previous contents of the HI register, and the $5 register contains the previous contents of the LO register. Because the contents of the 8-bit ACX register are loaded into a 32-bit register, the 8-bit value may be zero-extended to 32-bits before loading the HI register.

0044The MTLHX performs the inverse operation. For example, “MTLHX $5” loads the ACX register with the previous contents of the HI register, loads the HI register with the previous contents of the LO register, and loads the LO register with the contents of the $5 register.

0045The PPERM operation performs permutations as specified in a register, and stores the result in the ACX/HI/LO registers. For example, “PPERM $5, $6” causes the ACX/HI/LO registers to be shifted 6-bits to the left. Then, low-order six bits are selected from register $5 as specified by register $6. The 32-bit contents of register $6 are used to select which bits of register $5 will be used to fill the low-order bits of the ACX/HI/LO registers. Since there are 32 bits in register $5, 5 bits are needed to specify a specific one of the 32 bits. For example, “01101” is binary for the number 13. Thus, these five bits may specify bit <b>13</b>. Similarly, “00000” is binary for 0 and “11111” is binary for 31. Thus, all 32 bits may be specified using a 5-bit specifier.

0046Register $6 may specify the bits of $5 used to fill the low-order bits of ACX/HI/LO as follows: bits <b>0</b>–<b>4</b> are used to specify the source of bit <b>0</b>, bits <b>5</b>–<b>9</b> are used to specify bit <b>1</b>, bits <b>10</b>–<b>14</b> are used to specify bit <b>2</b>, bits <b>15</b>–<b>19</b> are used to specify bit <b>3</b>, bits <b>20</b>–<b>24</b> are used to specify bit <b>4</b>, and bits <b>25</b>–<b>29</b> are used to specify bit <b>5</b>. The remaining bits, <b>30</b>–<b>31</b>, may be unused. Thus, the instruction is performed using the specifiers as described to fill the lowest 6 bits of the LO register with the specified bits from the $5 register.

0047Finally, MULTP may be used to perform binary polynomial multiplication and MADDP may be used to perform binary polynomial multiplication with the result added to the ACX/HI/LO registers. These operations are analogous to MULT and MADD, but operate on binary polynomial operands.

0048The polynomial operands of MULTP and MADDP are encoded in 32-bit registers with each bit representing a polynomial coefficient. For example, the polynomial “x⁴+x+1” would be encoded as “10011” because the coefficients of x³and x²are “0” and the remaining coefficients are “1”. The MULTP instruction performs binary polynomial multiplication on two operands. For example, <br />(<i>x</i>⁴<i>+x+</i>1)(<i>x</i>+1)=<i>x</i>⁵<i>+x</i>⁴<i>+x</i>²+2<i>x</i>+1.<br /> Reducing the polynomial modulo two, yields x⁵+x⁴+x²+1. If the polynomials are encoded in the binary representation above, the same multiplication may be expressed as (10011)(11)=110101.

0049The MADDP instruction performs multiplication just as MULTP, adding the result to the ACX/HI/LO registers. Polynomial addition may be performed using a bitwise XOR. For example, the binary polynomial addition (x⁴+x+1)+(x+1) yields x⁴+2x+2. Reducing the coefficients modulo 2 yields x⁴which may be expressed as “10000”.

0050Referring to <figref idref="DRAWINGS">FIGS. 2 and 3</figref>, MDU <b>2020</b> receives two 32-bit operands, RS and RT. Using these operands, MDU <b>2020</b> performs a requested operation and stores a result in registers ACX <b>2021</b>, HI <b>2022</b>, and LO <b>2023</b>. Major data paths that may be used to perform these operations are shown in <figref idref="DRAWINGS">FIG. 3</figref>. The RShold register <b>3010</b> and the RThold register <b>3012</b> are used to hold the RS and RT operands. Multiplexers <b>3020</b>, <b>3022</b>, and <b>3024</b> are used to select whether to use the RS and RT operands directly or to use the values stored in the RShold register <b>3010</b> and the RThold register <b>3012</b>. Additionally, multiplexer <b>3022</b> may be used to select between the low-order and high-order bits of RT or the value stored in the RThold register <b>3012</b>.

0051The RThold register <b>3012</b> is connected to multiplexer <b>3022</b>. Multiplexer <b>3022</b> produces a 16-bit result by selecting the high-order bits of RThold <b>3012</b>, the low-order bits of RThold <b>3012</b>, the high-order bits of the RT operand, or the low-order bits of the RT operand. The output from multiplexer <b>3022</b> is processed by Booth recoder <b>3040</b> and stored in register RTB <b>3042</b>. Booth recoding is a technique that permits the multiplier array to treat signed and unsigned operands the same. The output of register RTB <b>3042</b> becomes the input SEL <b>3034</b> to array unit <b>3030</b>.

0052Array unit <b>3030</b> is used to perform arithmetic and binary polynomial multiplication as described below with reference to <figref idref="DRAWINGS">FIG. 4</figref>. Array unit <b>3030</b> takes as inputs ACC<b>1</b><b>3031</b>, ACC<b>2</b><b>3032</b>, M <b>3033</b>, SEL <b>3034</b>, and RThold <b>3012</b>. Inputs ACC<b>1</b><b>3031</b> and ACC<b>2</b><b>3032</b> are accumulated results used for operations that perform a multiplication and add or subtract the resulting value from an accumulated result. The inputs SEL <b>3034</b> (determined by register RTB <b>3042</b>) and M <b>3033</b> (determined by register RShold <b>3010</b>) form the operands for arithmetic operations. The inputs RThold <b>3012</b> (or the high-order or low-order bits of RThold <b>3012</b>) and M <b>3033</b> (determined by RShold <b>3010</b>) form operands for polynomial operations and permutations. Combinations of these inputs are used to perform various calculations as described in detail below.

0053Array unit <b>3030</b> also includes two outputs, ResultC <b>3035</b> and ResultS <b>3036</b>. In performing arithmetic operations, carry-save adders (CSAs) may be used to build a multiplication array. Carry-save adders calculate sums and carries separately to produce two outputs. Thus, ResultC <b>3035</b> and ResultS <b>3036</b> represent respectively, the carry and the sum outputs of a CSA multiplier array. In one implementation, ACC<b>1</b><b>3031</b>, ACC<b>2</b><b>3032</b>, ResultC <b>3035</b>, and ResultS <b>3036</b> are each 72 bits long and the remaining inputs are at most 32 bits long. Inputs ACC<b>1</b><b>3031</b> and ACC<b>2</b><b>3032</b> may be selected using multiplexers <b>3037</b> and <b>3038</b>.

0054Multiplexers <b>3050</b> and <b>3052</b> are used to select values as inputs to registers CPAA <b>3054</b> and CPAB <b>3056</b>. For example, multiplexer <b>3050</b> may be used to select between ResultC <b>3035</b>, the output of CPA <b>3058</b>, or the output of multiplexer <b>3020</b> (i.e., operand RS or RShold <b>3010</b>). Similarly, multiplexer <b>3052</b> may be used to select between ResultS <b>3036</b>, the value 0. and the output of multiplexer <b>3024</b> (i.e., operand RT or the output of CPAA <b>3054</b> and CPAB <b>3056</b>). These registers store the inputs to carry-propagate adder (CPA) <b>3058</b>. CPA <b>3058</b> may be used to complete multiplication operations (multiplies) and to perform iterative division operations (divides) as discussed below.

0055Register RDM <b>3060</b> stores the result of CPA <b>3058</b>. Finally, multiplexers <b>3070</b> and <b>3072</b> select which values form the result to be loaded into registers ACX, HI, and LO. Multiplexer <b>3070</b> may be used to select the ACX/HI/LO registers, RDM <b>3060</b>, or the result of CPA <b>3058</b>. Multiplexer <b>3072</b> may be used to instead load various permutations of the result selected by multipexer <b>3070</b>. Multiplexer <b>3072</b> is used to perform various rotations and loads of the ACX/HI/LO registers by permitting selection of the following values (forming 72-bit values when concatenated): (1) ahl, the 72-bit output of multiplexer <b>3070</b>; (2) arl, the 8 high-order bits of multiplexer <b>3070</b>, the contents of RShold <b>3010</b>, and the 32 low-order bits of multiplexer <b>3070</b>; (3) ahr, the 40 high-order bits of multiplexer <b>3070</b> and the contents of RShold <b>3010</b>; (4) hlr, the 40 low-order bits of multiplexer <b>3070</b> and the contents of RShold <b>3010</b>; and (5) 0ah, the 40 high-order bits of multiplexer <b>3070</b> (with 32 leading zeros).

0056The HI/LO registers are used to store the results of multiplication and to provide support for accumulator operations. In one implementation, the precision of the HI/LO registers is increased by adding register ACX as an extended accumulator. Thus, the ACX/HI/LO registers may store a 72-bit value. The corresponding data paths shown in <figref idref="DRAWINGS">FIG. 3</figref> and the accumulator capabilities of arrays <b>3030</b> also may be increased to support 72-bit values. Some operations cause the values stored in the result registers ACX, HI, and LO to be overwritten. For this reason, a separate result register <b>3080</b> may be provided to store the high-order and low-order result without the accumulator ACX.

0057Because the extended precision accumulator ACX/HI/LO may have higher precision than the general-purpose registers, it is not possible to load all 72 bits into a general-purpose register. Thus, it is desirable to provide instructions to support loading and manipulating the contents of the ACX/HI/LO registers (e.g., MFLHXU and MTLHX).

0058The data path described below includes six major parts: (1) input registering and selection; (2) Booth recoding; (3) multiplier arrays and permutation logic; (4) a carry propagate adder; (5) result registering and selection; and (6) a separate 32-bit output register for presenting results.

0059Input registering and selection is performed using the RShold and RThold registers to hold the RS and RT operands. Multiplexers select whether to use these operands directly or to use the registered versions. Booth recoding is performed on half of the RT operand at a time to provide inputs to the multiplier arrays and permutation logic.

0060Booth recoding is a technique that permits the multiplier array to treat signed and unsigned operands the same. This technique “recodes” operands as a subtraction from the next highest power of two. For example, 7 may be Booth recoded as follows: 8−1=1000₂−0001₂=100 <o ostyle="single">1</o>, wherein <o ostyle="single">1</o> represents −1. Hennessy and Patterson describe Booth recoding in Appendix A of “Computer Architecture: A Quantitative Approach,” Morgan Kaufmann Publishers, Inc. (1996), which is hereby incorporated by reference in its entirety for all purposes.

0061One array of array unit <b>3030</b> performs arithmetic multiplication and one array of array unit <b>3030</b> performs binary polynomial multiplication. In one implementation, both arrays are 32 bits by 16 bits (32×16) and are used once or twice depending on the size of the RT operand (i.e., an appropriate array is used once when RT is 16 bits long and twice when 32 bits long). The CPA may be used to complete multiplies and perform iterative divides. Other implementations may include faster mechanisms for performing divides.

0062The arithmetic multiplication array may be implemented using any of the techniques described by Hennessy and Patterson in the incorporated “Computer Architecture: A Quantitative Approach” Morgan Kaufmann Publishers, Inc. (1996). For example, Appendix A of Hennessy and Patterson describes several ways to speed up arithmetic multipliers. Any of the described techniques may be used as a basis for the polynomial multiplication extensions described below.

0063Referring to <figref idref="DRAWINGS">FIG. 4</figref>, array unit <b>3030</b> includes two parallel multipliers (Marray <b>4100</b> and MParray <b>4200</b>) and permutation logic <b>4300</b>. The first array, Marray <b>4100</b>, performs arithmetic multiplication as described below with reference to <figref idref="DRAWINGS">FIG. 5</figref>. Marray <b>4100</b> uses the following inputs as described above: ACC<b>1</b><b>3031</b>, ACC<b>2</b><b>3032</b>, M <b>3033</b>, and SEL <b>3034</b>. The outputs include ResultC <b>3035</b> and ResultS <b>3036</b>. The second array, MParray <b>4200</b>, performs binary polynomial multiplication as described below with reference to <figref idref="DRAWINGS">FIG. 6</figref>. MParray <b>4200</b> uses the following inputs as described above: the low-order bits of RThold <b>3012</b> or the high-order bits of RThold <b>3012</b>; RShold <b>3010</b>; and ACC<b>1</b><b>3031</b>. The output of MParray <b>4200</b> is ResultC <b>3036</b>. Finally, permutation logic <b>4300</b> is used to perform various permutations on the low-order bits of RShold <b>3010</b> based on the value stored in RThold <b>3012</b>.

0064Referring to <figref idref="DRAWINGS">FIG. 5</figref>, Marray <b>4100</b> is a 32-bit by 16-bit Wallace tree multiplier array that has been modified to support the addition of two 72-bit wide operands ACC<b>1</b> and ACC<b>2</b>. The ACC<b>1</b> and ACC<b>2</b> operands hold a carry-save representation of a 72-bit value. Because additions are already performed to carryout multiplications (i.e., by the carry-select adders (CSAs)), an additional adder may be included to all ACC<b>1</b> and ACC<b>2</b> to be added to intermediate results of multiplications. Marray <b>4100</b> generates a 72-bit wide result in a carry-save representation. Since 32×16 bits are processed per cycle, two passes through the array are required for 32×32 bit multiplies.

0065Marray <b>4100</b> is implemented as a Wallace tree built from arrays of carry-save adders. The width of these arrays may vary. This design may be implemented using an automated place and route rather than using data path style. Because the accumulate value from the previous array pass is input late into the array, the accumulate value does not need to come directly from a register. Booth recoding is performed using the method of overlapping triplets to more efficiently process multiplications. The output of Booth recoding tells whether to add operand M multiplied by −2, −1, 0, 1, or 2 for each power of 4. The multiplexers on the top-level CSA inputs are used to select the corresponding multiple of M.

0066Marray <b>4100</b> accumulates eight products from the Booth recoding plus one special partial product. The latter may be used for 32-bit unsigned calculations using the “0” and “1x” choices from the multiplexers. Within the Wallace tree, operands may be sign-extended to properly accumulate 2's complement results.

0067Referring to <figref idref="DRAWINGS">FIG. 6</figref>, binary polynomial-based multiplication operations are processed similarly to corresponding unsigned arithmetic operations. In one implementation, MParray <b>4200</b> is a 32×16 bit array that also performs an addition using exclusive-or (XOR) on an operand, for example, ACC<b>1</b>. As with Marray <b>4100</b>, 32×16 bits are processed per cycle and two passes through the array may be used for 32×32 multiplies. In the first cycle, ACC<b>1</b> is zero (for a MULTP operation) or the previous result (for a MADDP operation). In a second cycle, ACC<b>1</b> is the high order bits of the output from the first cycle.

0068MParray <b>4200</b> multiplies two operands (e.g., OpA and OpB) using an array with each row formed by taking the AND of OpA and a bit of OpB. For example, the first row is the logical AND of OpA and bit <b>0</b> of OpB. Row two is the logical AND of OpA and bit <b>1</b> of OpB. The result of each successive row is shifted one bit to the left. The final result is formed by taking the exclusive-or (XOR) of each column. Because a bitwise XOR may be used to perform addition in binary polynomial arithmetic, an accumulator row may be added to array MParray <b>4200</b> to support instructions such as MADDP.

0069Three multiplexers shown in <figref idref="DRAWINGS">FIG. 4</figref> are used to select either zero or the sum output of Marray <b>4100</b> to form ResultS <b>3036</b>; and the output of Marray <b>4100</b>, MParray <b>4200</b>, or permutation logic <b>4300</b> to form ResultC <b>3035</b>.

0070Referring again to <figref idref="DRAWINGS">FIG. 1</figref>, MDU <b>2020</b> starts a computation in the first cycle of the execute stage of the pipeline <b>1003</b>. If the calculations complete before the instruction has moved past the memory stage <b>1004</b> in the pipeline, then the result is held at that point. If the operation completes when the instruction has been moved past the memory stage <b>1004</b> in the pipeline, then the instruction has been committed and the results are written directly to the ACX/HI/LO registers.

0071The MDU <b>2020</b> is decoupled from the environment pipeline; it does not stall with the environment. That is to say the MDU <b>2020</b> will continue its computation during pipeline stalls. In this way, multi-cycle MDU operations may be partially masked by system stalls and/or other, non-MDU instructions.

0072<figref idref="DRAWINGS">FIG. 7A</figref> shows the pipeline flow through MDU <b>2020</b> for 32×16 bit multiplies. RS and RT arrive late, so the first cycle may be used for Booth recoding. The second cycle is where the array is run and the third cycle is where the CPA <b>3058</b> completes the computation. Because the results are always accessible to reads by MFxx instructions, 32×16 multiplies may be run without stalls. A 32×16 MUL, which returns the result directly to a general-purpose register (GPR) may stall for one cycle.

0073Referring to <figref idref="DRAWINGS">FIG. 7B</figref>, for 32×32 bit multiplies, the array is used twice, which adds one extra clock cycle to the 32×16 bit multiplications. As the first array pass is completing for the first portion of operand RT, Booth recoding is performed on the second portion of the operand. Thus, the Booth recoded portion of RT is available to begin the second pass through the array immediately after the first pass is complete. The multiplication result is then calculated using CPA <b>3058</b>.

0074Referring to <figref idref="DRAWINGS">FIG. 7C</figref>, a simple non-restoring division algorithm may be used for positive operands. The first cycle is used to negate RS, if needed. For timing reasons, this cycle is taken even if RS is positive. Following that, 32, 25, 18, or 10 cycles of iterative add/subtract operations are performed. The actual number is based on the amount of leading zeros on the positive RS operand. A final remainder adjust may be needed if the remainder was negative. For timing reasons, this cycle is taken even if the remainder adjust is not needed. Finally, sign adjustment is performed if needed on the quotient and/or remainder. If both operands are positive, this cycle may be skipped.

0075In one implementation, target applications demand fast division. Many techniques may be used to increase the performance of division. For example, the Sweeney, Robertson, and Tocher (SRT) algorithm or some variation thereof may be used.

0076Referring to <figref idref="DRAWINGS">FIG. 8</figref>, multiplication operations are implemented using a finite state machine. Multiplication begins in IDLE state <b>8010</b>. The multiplier stays in the idle state until the start signal is asserted. The multiplier then transitions to either the ARR<b>1</b> state <b>8020</b> or the ARR<b>2</b>A state <b>8030</b> depending on whether operand RT contains a 32-bit or 16-bit value. If a 16-bit value is stored in RT, then the system transitions to state ARR<b>2</b>A <b>8030</b> where the first array pass is run. Then, the multiplier transitions to state ARR<b>2</b>B <b>8040</b> where the second array pass is run. If a 16-bit value is stored in operand RT, the multiplication is run through the array unit in state ARR<b>1</b><b>8020</b>.

0077In this implementation, the multiplier is pipelined. One multiplication may be run through the array unit and another through the CPA. Thus, the multiplier either transitions from ARR<b>1</b><b>8020</b> or ARR<b>2</b>B <b>8040</b> to state CPA <b>8050</b> if there is no additional multiplication to perform, or begins a second multiplication. If no additional multiplication is needed, the multiplier is run through CPA <b>8050</b> and then either returns to IDLE <b>8010</b> or begins a new multiplication as discussed above.

0078If a second multiplication is ready to be performed when the first multiplication is ready to be run through the CPA, then the multiplier either transitions to CPA<b>1</b><b>8060</b> (for a 32×16 multiplication) or CPA<b>2</b>A <b>8070</b> (for a 32×32 multiplication). In state CPA<b>1</b><b>8060</b>, the first multiplication is run through the CPA and the second multiplication is run through the array unit. The multiplier then transitions to state CPA <b>8050</b> to finalize the second multiplication.

0079If the second multiplication is a 32-bit multiplication, then in state CPA<b>2</b>A <b>8070</b> the first multiplication is run through the CPA and the second multiplication is run through the array unit. The multiplier then transitions to state ARR<b>2</b>B <b>8040</b> to complete the 32×32 multiplication. This pipelined approach allows 32×16 multiplications to be issued every clock cycle, with a two-cycle latency. Also, 32×32 multiplications may be issued every other clock cycle, with a three-cycle latency.

0080Referring to <figref idref="DRAWINGS">FIG. 9</figref>, iterative division operations may be implemented using a finite state machine. In one implementation, the MDU begins in IDLE state <b>9010</b>. When a signal is received to begin a division operation, the MDU either transitions to DIV<b>1</b><b>9020</b> if the operation is signed or DIV<b>1</b>U <b>9030</b> if the operation is unsigned. States DIV<b>1</b><b>9020</b> and ERLY <b>9040</b> are used to prepare signed operands for division, adjusting the signs as necessary. States DIV<b>1</b>U <b>9030</b> and ERLYU <b>9050</b> are used to prepare an unsigned division operation. In states ERLY <b>9040</b> and ERLYU <b>9050</b>, leading zeros are detected in operand RS to adjust the number of division iterations necessary.

0081Iterative division is performed in states DIV <b>9060</b> and DIVU <b>9070</b>. Division may be performed by using a series of iterative add/subtracts and shifts. Finally, the remainders are finalized in states REM <b>9080</b> and REMU <b>9090</b>. If either of the operands is negative, sign adjustment is performed in state SGN <b>9100</b>.

0082Referring again to <figref idref="DRAWINGS">FIG. 4</figref>, in one implementation, permutation logic <b>4300</b> is used to support the PPERM instruction described above. Permutation logic <b>4300</b> consists of 6 single bit <b>32</b>:<b>1</b> selectors that may be used to select any of the 32 bits of RShold <b>3010</b> based on the value of RThold <b>3012</b>. This logic may be implemented directly in the data path module.

0083For example, permutation logic <b>4300</b> may be used to execute the instruction “PPERM $5, $6”. Permutation logic <b>4300</b> uses 6 5-bit selectors determined by RThold <b>3012</b> to identify which bits to include as output from RShold <b>3010</b>. For example, if register $5 contains the low-order bits “010101”, then the selector “00010” would choose bit <b>2</b> (i.e., the third bit from the right) containing “1”. If RThold <b>3012</b> contains the low-order bits “0001000011”, then bit <b>2</b> (containing a “1”) and bit <b>3</b> (containing a “0”) will be selected yielding “10”. Using this method, permutation logic <b>4300</b> may select bits from RShold <b>3010</b> to generate 6 bits based on RThold <b>3012</b>. The resulting 6 bits concatenated to the 66 low-order bits of ACC<b>1</b> to form the result. This effectively shifts the 66 low-order bits of ACC<b>1</b> six bits to the left and replaces the 6 low-order bits with the output of the permutation logic <b>4300</b>.

0084In addition to multiplier implementations using hardware (e.g., within a microprocessor or microcontroller), implementations also may be embodied in software disposed, for example, in a computer usable (e.g., readable) medium configured to store the software (i.e., a computer readable program code). The program code causes the enablement of the functions or fabrication, or both, of the systems and techniques disclosed herein. For example, this can be accomplished through the use of general programming languages (e.g., C, C++), hardware description languages (HDL) including Verilog HDL, VHDL, AHDL (Altera HDL) and so on, or other available programming and/or circuit (i.e., schematic) capture tools. The program code can be disposed in any known computer usable medium including semiconductor, magnetic disk, optical disk (e.g., CD-ROM, DVD-ROM) and as a computer data signal embodied in a computer usable (e.g., readable) transmission medium (e.g., carrier wave or any other medium including digital, optical, or analog-based medium). As such, the code can be transmitted over communication networks including the Internet and intranets.

0085It is understood that the functions accomplished and/or structure provided by the systems and techniques described above can be represented in a core (e.g., a microprocessor core) that is embodied in program code and may be transformed to hardware as part of the production of integrated circuits. Also, the systems and techniques may be embodied as a combination of hardware and software. Accordingly, other implementations are within the scope of the following claims.